Who is the Best Player Ever? A Complex Network Analysis of the History of Professional Tennis
In this academic paper, they determine the best tennis player in the history of professional tennis. How do they do this? They use a modified version of Googles PageRank. When you look at a professional sports league you can see that it is very similar to a network or set of webpages. Each team is linked to other teams through matches, tournaments and other teams results. In class we learned about PageRank and each nodes rank being determined by the number of links in and out of each node. Similar to this, each Tennis player was considered a node and the number of wins (link going in) and loses (link going out) helped determine their rank. Additionally, each person they won or lost against had their own ranking that factored into node n’s ranking. This is a very simple explanation to a little bit more complex network (considers time period and surface played on) but the general idea is the same as the PageRank we learned about in class. In the end, each player converged to a “prestige score” (equivalent to the PageRank score at equilibrium) that was used to rank the players. The best tennis player in the history of professional tennis—Jimmy Connors—pretty accurate algorithm.
Throughout the paper, they compared their ranking technique to the traditionally ranking technique used in professional tennis. They found, that the modified PageRank algorithm was far more accurate and predictable than the traditional techniques. Why? Because the PageRank method doesn’t require external input. It is purely based on statistics. Each player’s “prestige score” is determined by comparison to every other player, past performances and total number of victories. They compared the ranking from the PageRank algorithm to the rankings from the Association of Tennis Professionals. What they found was that the “prestige score” did a better job at accounting for the career length of a Tennis Player and the importance of each win. For example, a recently talented athlete—Rafael Nadal—isn’t ranked very high on the ATP rankings because he is fairly new. However, the prestige score takes that into account and ranks him higher (most likely a more accurate ranking).
Professional tennis players are just one application of PageRank. It can be applied to almost anything that can be represented as a graph—viruses (sickness and CS related), other sport leagues such as soccer, the NFL, NCAA sports. Not only does PageRank provide a more accurate representation of true rankings but it is also rather easy to implement. You no longer need to be an expert in mathematics to get an accurate representation of your favorite sport.
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0017249